US4404646A - Piping network analog apparatus - Google Patents
Piping network analog apparatus Download PDFInfo
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- US4404646A US4404646A US06/220,287 US22028780A US4404646A US 4404646 A US4404646 A US 4404646A US 22028780 A US22028780 A US 22028780A US 4404646 A US4404646 A US 4404646A
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- compressor
- voltage
- piping
- scaling
- capacitor pump
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06G—ANALOGUE COMPUTERS
- G06G7/00—Devices in which the computing operation is performed by varying electric or magnetic quantities
- G06G7/48—Analogue computers for specific processes, systems or devices, e.g. simulators
- G06G7/64—Analogue computers for specific processes, systems or devices, e.g. simulators for non-electric machines, e.g. turbine
Definitions
- This invention relates to apparatus for simulating the low frequency pulsations and surge characteristics of centrifugal compressors and pumps and their interaction with their piping systems.
- Centrifugal compressors have been widely used in pumping gaseous fluids through piping systems, especially in the transportation of natural gas through pipelines.
- a centrifugal compressor can either amplify or attenuate external pulsations.
- the severe pulsation frequencies normally relate to one of the major pipe resonances of the piping systems, and measurements along the piping show a strong standing wave pattern, often existing across or through the compressor.
- the onset, frequency, and severity of machine surge can also vary as the piping system is changed.
- Pulsation levels are most severe when the compressor is situated at or near a velocity maximum (pressure minimum) in the pulsation standing wave field.
- a nonlinear analog is provided to be operated in such a manner that, in effect, the dynamic flow impedance characteristics of a piping system is superimposed upon the compressor curves and the combined characteristics are used to predict pulsation gain or loss and system stability and the effect of various variables upon them.
- FIG. 1 is a plot of flow versus discharge pressure illustrating the basic nonlinear nature of pipe flow resistance
- FIG. 2 is a plot of flow versus discharge pressure illustrating the effect of pressure modulation upon flow
- FIG. 3 is a plot of impedance versus length for the resonance mode of a fundamental half wave in a pipe or vessel closed at both ends;
- FIG. 4 is a plot of discharge pressure versus flow, which illustrates the effect of the slope of the dynamic load line upon the stability of the system
- FIG. 5 is a plot of mass or flow volume versus compressor discharge pressure into a reactive piping system
- FIG. 6 is a plot illustrating the surge orbit pattern for the reactive system of FIG. 5.
- FIG. 7 is a schematic illustration of the preferred embodiment of the centrifugal compressor analog of the present invention.
- the operating point In all cases, the operating point must fall on the pipe impedance curve so long as steady flow conditions are assumed and the pipe steady flow impedance is not changed. If, however, flow is modulated at higher frequencies where inertial effects and line pack effects are significant, then the steady state impedance curve sets the operating point but no longer controls the relation between pulsation pressures and flows. This results in a different impedance line drawn to the operating point and the slope of this dynamic impedance line is quite frequency sensitive for typical piping systems.
- the dynamic impedance frequency line is shown in FIG. 2 as line 12.
- the operating curves 13, 14 and 15 are shown for a centrifugal compressor operating at an average suction pressure P S0 but pressure modulations cause this to vary from P S1 to P S2 .
- the slope of the dynamic impedance line 12 in FIG. 2 can be any positive value, theoretically, from near zero to a very high value, depending on pulsation frequency and transient response characteristics of the discharge piping.
- FIG. 3 illustrates a plot of impedance versus length for the resonance mode of a fundamental half wave in a pipe or vessel closed at both ends.
- the slope of the dynamic impedance line will vary from a relatively high value at the ends of the vessel to essentially zero at the center of the vessel.
- a compressor feeds such a vessel at its center point
- a very low impedance would be evidenced at the frequency depicted.
- a very high impedance would be seen at feed points near the closed ends. Therefore, the magnitude of the dynamic impedance would vary markedly depending upon where the compressor feeds into the vessel and upon the perturbation frequency.
- Compressor surge has at times been a problem. To illustrate this, consider a set of compressor curves as shown in FIG. 4 with the operating point B and a dynamic load line as shown at Z 1 . If the suction pressure is modulated from P 1 to P 2 , the system is stable since in all cases the compressor head is sufficient to supply the discharge pressure required by the dynamic load line. However, if suction pressure drops below P 3 , then the compressor cannot supply the piping pressure required to supply the necessary flow and flow therefore diminishes. As flow diminishes, the compressor head inadequacy becomes more pronounced and the entire flow regime collapses and surge results. The piping may begin to backflow locally into the compressor discharge to make up for the compressor inadequacy. As the suction pressure rises, then the compressor rebuilds up the load line into a temporary stable condition, but with a rather violent flow surge. The cycle then repeats.
- FIG. 5 illustrates a condition which can be achieved only in idealized piping systems.
- FIG. 5 illustrates a condition which can be achieved only in idealized piping systems.
- FIG. 5 illustrates a condition which can be achieved only in idealized piping systems.
- FIG. 5 illustrates a condition which can be achieved only in idealized piping systems.
- FIG. 5 illustrates a condition which can be achieved only in idealized piping systems.
- FIG. 5 illustrates a condition which can be achieved only in idealized piping systems.
- FIG. 5 illustrates the orbit of flow versus pressure into a reactive piping system.
- the orbit of FIG. 5 for a reactive system is comparable to the line Z 3 in FIG. 4 for a non-reactive system, i.e. a state of stability.
- FIG. 6 illustrates a surge orbit pattern for the reactive system of FIG. 5.
- the complexity of FIGS. 5 and 6 illustrate the need for simulating the various interactions of parameters of the compressor and piping system.
- an analog is provided to simulate the operation of a centrifugal compressor utilizing an actual (non-linear) head curve in order to, among other things, simulate surge instability frequencies and amplitudes.
- a conventional capacitor pump when driven by a sinusoidal voltage proportional to the sum of at least 3, and preferably 5 values, will simulate the dynamic characteristics of a centrigual compressor.
- the input and output of the analog are connected to suitable delay lines and the like to simulate various piping configurations, the interaction of the compressor with the piping system can be simulated.
- FIG. 7 there is shown a conventional capacitor pump comprising the diodes D 1 and D 2 and the capacitor C 0 , one form of which is described in the U.S. Pat. No. 2,951,638 along with the attendant delay lines for simulating a piping system.
- a capacitor pump for simulating the pumping action of a centrifugal compressor and having circuits (not shown) connected to the input and output analogizing the piping upstream and downstream of the compressor.
- Means are also supplied for applying a voltage to the input of the capacitor pump which is proportional to the suction pressure of the compressor, this means being indicated by “Suction E s ".
- means are provided for applying a voltage to the output of the capacitor pump proportional to the discharge pressure and indicated by the term “Discharge E d ".
- F S and F d are low pass filters which are inserted to filter out any stray alternating currents which may have an adverse effect on the capacitor pump.
- the driving means has a sinusoidal voltage output which is proportional to the sum ##EQU1##
- the driving means includes a first means for sensing the suction voltage here shown as amplifier A2. Means are also provided for scaling the output of the first means (A2) by a first factor (B-1), here illustrated as the potentiometer B, to yield the value (B-1) E s in equation (1). (B-1) is derived by appropriate feed back around amplifier A2 as shown from the resistor network 9R and R.
- Means are also provided for sensing and scaling the current flow through the capacitor pump by a second factor: ##EQU2## to yield the value ##EQU3## where C is a numerical coefficient and C 0 is the value of capacitance C 0 in the circuit.
- This means is illustrated as including the amplifier A8 and potentiometer alpha. The latter is set in accordance with the calculated value of equation (2) above.
- the components within the dashed block labeled "METER” is a Hall effect metering circuit fully described in copending application Ser. No. 94,507, filed Nov. 15, 1979 to which reference is made for further details and the disclosure of which is incorporated by reference in full herein.
- the current flowing to amplifier A8 is directly proportional to the current flowing through the capacitor pump.
- means are also provided for squaring and scaling the current flow through the capacitor pump to obtain the value:
- This means includes a potentiometer D for scaling the current being fed to amplifier A1 and a wide band precision analog multiplier M1 which squares the current value multiplied by the factor D.
- Means are also provided for scaling a constant voltage by a fourth factor which includes a constant voltage source V cc , and a scaling potentiometer A to obtain value A.
- Means are also provided for multiplying the suction voltage E s by the current flowing through the capacitor pump and scaling the result by a fifth factor E to obtain the value:
- Means are also provided for adding the foregoing values in accordance with equation (1) to provide a sum voltage E B .
- This means of addition includes resistors R A , R B , R C , R D and R E hooked into an adding circuit as shown and amplifier A7.
- the various factors involved in these means are selected to define the coefficient of the terms of the above equation which equation in turn defines the sum voltage required for the electrical driving means to cause the capacitor pump to simulate the behavior of the centrifugal compressor.
- the sum voltage is applied to a broad band precision analog multiplier M3 where the sum voltage is multiplied by a sinusoidal voltage EG of constant magnitude and frequency.
- the sinusoidal voltage fed to amplifier A5 has an ampitude proportional to the sum voltage.
- the amplifiers A1 through A9 all be wide band precision analog amplifiers.
- a current modulator CM can be provided as shown in FIG. 7 and an oscilloscope connected as shown to display the output of the capacitor pump.
- the current modulator causes a periodic variation in current flow and provides an analog voltage output which is proportioned to such current, which voltage is used to drive the X-axis of the oscilloscope.
- the Y-axis is driven directly by E d .
- the various coefficients of equation 1 can be adjusted in the circuit of FIG. 7 to force conformance of the capacitor pump output curve, which is E d , to the desired head or performance curve.
Abstract
Description
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Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
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US06/220,287 US4404646A (en) | 1980-12-29 | 1980-12-29 | Piping network analog apparatus |
Applications Claiming Priority (1)
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US06/220,287 US4404646A (en) | 1980-12-29 | 1980-12-29 | Piping network analog apparatus |
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US4404646A true US4404646A (en) | 1983-09-13 |
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US06/220,287 Expired - Fee Related US4404646A (en) | 1980-12-29 | 1980-12-29 | Piping network analog apparatus |
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Cited By (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US4559610A (en) * | 1983-05-04 | 1985-12-17 | Southwest Research Corporation | Gas pumping system analog |
US5062068A (en) * | 1989-02-09 | 1991-10-29 | Kabushiki Kaisha Toshiba | Computerized analyzing system for piping network |
US20070150113A1 (en) * | 2005-12-02 | 2007-06-28 | Chi-Yi Wang | System of energy-efficient and constant-pressure parallel-coupled fluid-transport machines |
Citations (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US2951638A (en) * | 1955-05-31 | 1960-09-06 | Southern Gas Ass | Gas pumping system analog |
US3207889A (en) * | 1960-09-21 | 1965-09-21 | Naz Metanodotti S P A Soc | Analogue pipe network analyzer |
US3529144A (en) * | 1968-05-22 | 1970-09-15 | Marvin Leroy Patterson | Waveform generator for compressor flow simulation |
US3599233A (en) * | 1970-01-12 | 1971-08-10 | Richard W Meyer | Apparatus for analyzing pipeline networks and computing elements therefor |
-
1980
- 1980-12-29 US US06/220,287 patent/US4404646A/en not_active Expired - Fee Related
Patent Citations (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US2951638A (en) * | 1955-05-31 | 1960-09-06 | Southern Gas Ass | Gas pumping system analog |
US3207889A (en) * | 1960-09-21 | 1965-09-21 | Naz Metanodotti S P A Soc | Analogue pipe network analyzer |
US3529144A (en) * | 1968-05-22 | 1970-09-15 | Marvin Leroy Patterson | Waveform generator for compressor flow simulation |
US3599233A (en) * | 1970-01-12 | 1971-08-10 | Richard W Meyer | Apparatus for analyzing pipeline networks and computing elements therefor |
Cited By (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US4559610A (en) * | 1983-05-04 | 1985-12-17 | Southwest Research Corporation | Gas pumping system analog |
US5062068A (en) * | 1989-02-09 | 1991-10-29 | Kabushiki Kaisha Toshiba | Computerized analyzing system for piping network |
US20070150113A1 (en) * | 2005-12-02 | 2007-06-28 | Chi-Yi Wang | System of energy-efficient and constant-pressure parallel-coupled fluid-transport machines |
US7480544B2 (en) * | 2005-12-02 | 2009-01-20 | Wen-Cheng Huang | Operation method of energy-saving fluid transporting machineries in parallel array with constant pressure |
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